Why would you not add the 1 and 2 first, then multiply 3 x 3, subtract the 2 and arrive at 7 as the answer? In other words, is there a rule that says the multiplication must be the first part of the equation performed? I really don't know and am simply curious.

In other words, is there a rule that says the multiplication must be the first part of the equation performed?

Yep. It's taught differently in different places, but here in Scotland I learned the rule as BODMAS or BEDMAS, standing for Brackets, Exponentials, Division, Multiplication, Addition, Subtraction. The rule is called order of operations.

I'm closer to Jabb on this one .. I would always do the brackets first if there were any and then work left to right. My answer would be 2.5 LOL.

BODMAS is what is in the work now and is as Reeshy said. It's the first I've seen of it. I've only been looking at it this morning and have had a couple of problems

This one ...

(23-4+9)x(half - quarter) of 24 = ?

I got the answer 60 but the correct answer is 168 .. quite a difference!!!

SO we do brackets first .. and here is where I think I went wrong ... the BODMAS rule doesn't apply? Using the BODMAS rule in that first bracket you would get 10 (so 10 x 6 = 60)but if you do it left to right you get 28. (28 x 6 = 168)

I've never heard of BODMAS or BEDMAS before. I was taught "PEMDAS", meaning Parentheses, Exponents, Multiplication, Division, Addition, Subtraction. Same idea, just different word to remember it I guess.

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The bad thing about BODMAS/BEDMAS/PEMDAS is that it is easy to think that multiplication or division comes first, and that addition comes before subtraction.

Technically we learned P then E then M/D interchangeable then A/S interchangeable. I dunno, but math always just clicked for me so order of operations wasn't that difficult to keep straight. Math was by far my best subject...which kind of explains my desire to go to grad school for engineering. I missed all the math (and science) that I didn't get while I was an undergrad studying architecture.

But it's still that first bracket that I stuffed up ... I used the BODMAS rule within that bracket and got 10 but to get the right answer you DON'T use the rule .. you just work left to right.

I wrote it different to the paper and put the words to half and a quarter to get away from putting the / sign which I had used before to mean divide. In the book it is

(23-4+9)x(1/2 - 1/4) of 24 =

TO my way of thinking if he got the problem

23-4+9= the answer would be 10 using BODMAS

but as it's within that bracket the answer is 28.

I don't understand how you got 10 from 23-4+9?

How does 23-4+9 not equal 28?

I read it as 23-4= 19, 19+9=28, or if you like 23+9=32, 32-4=28, or even -4+9=5, 23+5=28.

Can you please explain how you got 10?

And with PEMDAS/BODMAS, as a general rule everything in the parentheses is done first. So you would compute both 23-4+9 and 1/2-1/4, before multiplying the two results together. Then once you're in the parentheses, you do all of the exponents first, then multiplication/division, then addition/subtraction. Then you'd do the second or third (or however many parenthetical phrases there are) before you do the operations between the parenthetical phrases. Make sense?

So for example:

(2^2 * 4 - 2) * (2 - 2^3) = ?

Starting with the first ( ), you do E first, so 2^2 = 4. Then M/D, 4 * 4 = 16. Then A/S, 16 - 2 = 14.Then with the second ( )...starting with E, 2^3 = 8. Then 2 - 8 = -6.Then you do the ( ) * ( ), so 14 * -6 = -84.So the overall order used in this case is P1, E1, M1, S1, P2, E2, S2, M(overall), where 1 and 2 refer to the 1st and second set of ( ).

In the special case where you'd have a term that is ( )^x, you would do everything inside the parentheses first as seen above, since P comes before E, and then you would apply the ^x to your final result from inside the ( ).

Because if you were supposed to do the addition first according to BODMAS?So 4+9= 1323-13=10

This morning I would have gotten 28 straight away and now this has *&^%$$# me right up.

I think what's confusing you in this case is the level of operation and the order of operation, though the terms are generally interchangeable.

Think of the levels as P, E, MD, and AS.

Think of the order as Left to Right. Within every LEVEL you then perform the ORDER.

So in the AS LEVEL, you have 23 - 4 + 9. You then look to the L to R ORDER. This means you do 23 - 4 first, because it's on the "left". then you do 19 + 9, because that's on the "right".

Still confused? I might be able to explain it another way if this doesn't clear it up So sorry you're frustrated.

Edit: Multiplication and Division are, in order of operation, Equals. Addition and Subtraction are also Equals. This means the BODMAS, or PEMDAS, could just as easily be written BOMDSA, or PEDMSA. The letters MD and AS appear in the order they do in BODMAS and PEMDAS, because they're easier to pronounce and therefore easier to remember.

Since M and D are equal, this means that one does not hold precedence over the other, 2/3*4/5 is the same as 2*4/3/5.

Since A and S are equal, this means that one does not hold precedence over the other, 1+2-3+4 is the same as 1+2+4-3.

Multiplying and dividing are one kind of thing, and are done first, before you touch any adding and subtracting. When deciding which of these to do first, you go left to right - multiplying does not come before dividing, unless it happens to be to dividing's left.

Adding and subtraction are another kind of thing, and are done after the multiplying and dividing. Again, once you are at the adding/subtracting phase of the question, you go left to right. Adding does not come before subtracting, unless it just works out that way.

Multiplying and dividing are one kind of thing, and are done first, before you touch any adding and subtracting. When deciding which of these to do first, you go left to right - multiplying does not come before dividing, unless it happens to be to dividing's left.

Adding and subtraction are another kind of thing, and are done after the multiplying and dividing. Again, once you are at the adding/subtracting phase of the question, you go left to right. Adding does not come before subtracting, unless it just works out that way.

Does that help, or does it confuse it further?

This is what I'm trying to get at, agony. It seems easy to me, but that's because I already understand how it works, and I use it all the time. Trying to teach someone else on the other hand just makes it feel so much more complicated.

Copago, I'm not sure I know how to explain it any other way. The best way I'd say to understand how to do it is just to work complicated multi-function problems over and over and over again, and sit down with someone who understands it and can work through the problems with you until it becomes second nature.

No no, I have it now. Thanks for the explanations Kaddarsgirl and Agony

I did have it at your first explanation, K, but had no idea how to explain that to a ten year old. I didn't want to start him off being confused by it all and not being able to recover from it!

Glad I could help I didn't mean to overload you with replies by the way. I just got so into it! Good luck with your ten year old I wouldn't want him to start off being so confused by it all either...that's how we get people who don't like math

Exactly! He's pretty good at maths and does it enjoy it so I wanted to make sure I had it right before trying it out on him.

I'd love to be able to show you the page that was sent out for him to do (I've scribbled all over it) - it shows FOUR ways of working out (left to right, working backwards, doing what you want and BODMAS)... I don't understand why we would show them how to do something, get them to do it and THEN tell them that is the wrong way to do it? It confused me and I'm a seemingly intelligent adult LOL

I don't understand why we would show them how to do something, get them to do it and THEN tell them that is the wrong way to do it? It confused me and I'm a seemingly intelligent adult LOL

That would confuse, and frustrate, the crap out of me too! That certainly, to me, doesn't seem like a very logical way to teach children math. They've got so much to learn anyway, it doesn't make sense to teach them something that's wrong and then tell them to forget it. Very strange indeed.

Your son is very lucky to have a parent like you who cares so much about him, as you clearly do